Premise 1. The
hypothesis of embedded cognition (HEMC) is a competitor to the hypothesis of
extended cognition (HEC) as a general philosophy of cognitive science, or at
least as a treatment of the cases that often motivate HEC (Rupert, "Challenges
to the Hypothesis of Extended Cognition," Journal
of Philosophy, 2004, pp. 395-97).

Intermediate
conclusion 2. Thus, we should accept Clark and Chalmers's endorsement of
HEC only if Clark and Chalmers provide a substantial argument in support of HEC
(i.e., only if they can show that other things are not equal).

Premise 3. Clark
and Chalmers offer two identifiable arguments in support of HEC, one intuitive
and commonsensical (the Otto's-notebook argument and the intuitive criteria
derived from it), the other an argument in philosophy of cognitive science (the
natural- or causal-explanatory-kinds argument) (ibid., pp. 401-07).

Premise 4. The
intuitive argument falls to a dilemma: either one accepts Clark and Chalmers's
conscious-endorsement criterion, effectively collapsing HEC into HEMC, or one
rejects the conscious-endorsement criterion leaving in place only the remaining
three criteria; but these are subject to obvious counterexamples—see
cases involving cognitive bloat (ibid., pp. 402-05).

Premise 5. The
natural-kinds argument falls to a different dilemma: either we individuate the
relevant causal-explanatory kinds in a fine-grained way, in which case Clark
and Chalmers's argument falls to the worries about fine-grained differences, or
we treat the relevant causal-explanatory kinds as coarse-grained—which I
called "generic"—kinds, which leads to bloat and also robs such kinds of
any causal-explanatory power not accommodated by HEMC (ibid., sections V-VIII;
for the two options – fine-grained v. coarse-grained kinds –
explicitly presented side-by-side, see pp. 407, 418-19, 424).

Conclusion. Therefore, we have no good reason to accept HEC,
given the current state of the evidence (ibid., pp. 428).

Note that this argument (a) does not presuppose that we've
identified the essence of any particular kind of mental state (we may have, but
the argument need not be so commital), (b) has nothing directly to do with what
has come to be known as the Parity Principle (issues to do with parity are
simply ignored, in favor of what I took to be the more pressing issue –
the sorts of characteristics that appear to do causal-explanatory work in
cognitive science), and (3) does not constitute a differences argument against HEC
(differences are emphasized in connection with one half of a dilemma that
criticizes one premise of one argument for HEC).